|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
gptkb:hyperbolic_plane
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:compact
|
true
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:fullName
|
gptkb:Projective_Special_Linear_Group_of_2x2_Real_Matrices
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:PGL(2,_R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PSL(2, R)
|
|
gptkbp:isLocallyIsomorphicTo
|
gptkb:SL(2,_R)
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonCompactSimpleLieGroup
|
true
|
|
gptkbp:isomorphicTo
|
orientation-preserving isometries of the hyperbolic plane
|
|
gptkbp:isQuotientOf
|
gptkb:SL(2,_R)
GL(2, R) by scalar matrices
center of SL(2, R)
|
|
gptkbp:isRealLieGroup
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isTopologicalGroup
|
true
|
|
gptkbp:Lie_algebra
|
gptkb:sl(2,_R)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realForm
|
gptkb:PSL(2,_C)
|
|
gptkbp:universalCover
|
universal covering group of PSL(2, R)
|
|
gptkbp:usedIn
|
gptkb:geometry
gptkb:hyperbolic_geometry
gptkb:Teichmüller_theory
complex analysis
differential geometry
dynamical systems
mathematical physics
modular forms
number theory
representation theory
automorphic forms
|
|
gptkbp:bfsParent
|
gptkb:Fuchsian_groups
gptkb:Hecke_group
gptkb:modular_group_PSL(2,_Z)
|
|
gptkbp:bfsLayer
|
6
|